Differences

This shows you the differences between two versions of the page.

Link to this comparison view

cs-401r:homework-0.2 [2014/09/03 06:00]
ringger created
cs-401r:homework-0.2 [2014/12/31 23:19] (current)
ringger
Line 1: Line 1:
-<​big>'''​Bayes Nets'''</​big>​+Bayes Nets =
  
 == Objectives == == Objectives ==
Line 24: Line 24:
 #* Assuming that the value of S is known, list ''​all''​ independence relations between T and other variables. ​ Be sure to consider all of the cases in which the other variables in the model have known values and when they do not. #* Assuming that the value of S is known, list ''​all''​ independence relations between T and other variables. ​ Be sure to consider all of the cases in which the other variables in the model have known values and when they do not.
 # [10 points] Factor the joint distribution represented by the entire model shown in the figure according to the explicit independence assumptions represented in the model. # [10 points] Factor the joint distribution represented by the entire model shown in the figure according to the explicit independence assumptions represented in the model.
-# [10 points] Write the four entries and their values in the conditional distribution for <​math>​P(L=0 | M=m,S=s)</​math> ​(for m in {0,1} and s in {0,1}). +# [10 points] Write the four entries and their values in the conditional distribution for $P(L=0 | M=m,S=s)(for m in {0,1} and s in {0,1}). 
-# [10 points] (a) Write an expression for the joint probability ​<​math>​P(T=1, R=0, L=0, M=0, S=1)</​math> ​in terms of the probabilities given in the model (use the symbolic forms). ​ (b) Then compute the actual probability. +# [10 points] (a) Write an expression for the joint probability ​$P(T=1, R=0, L=0, M=0, S=1)in terms of the probabilities given in the model (use the symbolic forms). ​ (b) Then compute the actual probability. 
-# [10 points] Compute ​<​math>​P(T=1, R=0, L=0)</​math>​. Show your work. +# [10 points] Compute ​$P(T=1, R=0, L=0)$. Show your work. 
-# [10 points] Compute ​<​math>​P(T=1 | R=0, L=0)</​math>​. Show your work.+# [10 points] Compute ​$P(T=1 | R=0, L=0)$. Show your work.
 # [10 points] Prove that the relationship we call conditional independence is symmetric. ​ Apply the same [[Proofs|standard of proof]] as in homework 0.1. # [10 points] Prove that the relationship we call conditional independence is symmetric. ​ Apply the same [[Proofs|standard of proof]] as in homework 0.1.
-#* In other words, show that (a) <​math>​P(X | Y, Z) = P(X | Z)</​math> ​if and only if <​math>​P(Y | X, Z) = P(Y | Z)</​math>​ +#* In other words, show that (a) $P(X | Y, Z) = P(X | Z)if and only if $P(Y | X, Z) = P(Y | Z)$ 
-#* Equivalently,​ show that (b) <​math>​P(X, Y | Z) = P(X | Z) \cdot P(Y|Z)</​math> ​if and only if <​math>​P(Y, X | Z) = P(Y | Z) \cdot P(X | Z)</​math>​ +#* Equivalently,​ show that (b) $P(X, Y | Z) = P(X | Z) \cdot P(Y|Z)if and only if $P(Y, X | Z) = P(Y | Z) \cdot P(X | Z)$ 
-#* (in other words, the "​given ​<​math>​Z</​math>​" stays the same, while <​math>​X</​math> ​and <​math>​Y</​math> ​trade places).+#* (in other words, the "​given ​$Z$" stays the same, while $Xand $Ytrade places).
 #* To be clear, prove (a) or (b). #* To be clear, prove (a) or (b).
  
cs-401r/homework-0.2.txt · Last modified: 2014/12/31 23:19 by ringger
Back to top
CC Attribution-Share Alike 4.0 International
chimeric.de = chi`s home Valid CSS Driven by DokuWiki do yourself a favour and use a real browser - get firefox!! Recent changes RSS feed Valid XHTML 1.0